A rectangle is inscribed in a right isosceles triangle, such that two of its vertices lie on the hypotenuse, and two other on the legs. What are the lengths of the sides of the rectangle, if their ratio is 5:2, and the length of the hypotenuse is 45 in? (Two cases)

CASE 1: (Blank) (blank) (Blank) (blank)
CASE 2: (Blank) (blank) (Blank) (blank)

(-9,11) This one is eleven units from the y-axis

(10,15) is fifteen units away

(5,-12) is 12 units away

(-4,14) is 14 units away

so the one closest to the y-axis is (-9,11)

Please mark me as brainliest

The above answer is wrong. Once graphing the lines you will see the -4 and 14 is the closet to the y axis

answer should be C

let me know if that’s right

Answer:

answer should be C

Step-by-step explanation:

I see no actual question, but I'm assuming that you want to find the dimensions of the rectangle.

In general, the area of a rectangle with width [tex]w[/tex] and length[tex]l[/tex] is

[tex] A = wl [/tex]

In this case, we know that the width is one-fourth of its length, which means [tex] w = \frac{1}{4}l[/tex]

If we plug this expression for w in the formula for the area, we get

[tex] A = wl = \dfrac{1}{4}l\cdot l = \dfrac{1}{4}l^2 [/tex]

We also know that the area is 9 squared units, so we have

[tex] 9 = \dfrac{1}{4}l^2 [/tex]

If we multiply both sides by 4, we get

[tex] l^2 = 36 [/tex]

Consider the square root of both sides (we only accept the positive solution, since a negative length would make no sense:

[tex] l = \sqrt{36} = 6 [/tex]

So, the length is 6, and the width is one-fourth of 6, i.e.

[tex]\dfrac{1}{4} \cdot 6 = \dfrac{6}{4} = \dfrac{3}{2} = 1.5[/tex]

Answer:

1.5

Step-by-step explanation:

Answer:

  B.  -1, 2, -4, 8

Step-by-step explanation:

The characteristic of a geometric sequence is that adjacent terms have a common ratio. Sequence B is the only one.

  2/-1 = -4/2 = 8/-4 = the common ratio: -2

___

Ratios of adjacent terms are different for the other sequences.

Answer:

A and D

Step-by-step explanation:

ΔACD is 3 times the size of ΔABE, so the dilation uses a scale factor of 3. That only leaves choices A, D, and E.

Dilation about point A leaves point A in the same place, so choice E can be eliminated on that basis. (There is only one point A, and not a translated version, consistent with choice A.)

Point C in the larger triangle corresponds to point B in the smaller triangle, and is 4 units down from it. Hence the description of D makes sense.

___

We hope you can see that choosing correct answers in multiple-choice questions is as much about consistency and reasonableness as it is about knowing how to work the problem. You do have to understand what the problem is asking and what the answers are saying about it.

To determine the number of each type of question on the math test, set up a system of equations. Solve the system of equations using substitution or elimination method. The math test consists of 5 multiple-choice questions and 15 problem-solving questions.

To determine how many of each type of questions are used on the math test, we can set up a system of equations. Let's use x to represent the number of multiple-choice questions and y to represent the number of problem-solving questions. Since there are 20 questions in total, we have the equation x + y = 20. Each multiple-choice question is worth 5 points and each problem-solving question is worth 6 points, so we also have the equation 5x + 6y = 100.

We can solve this system of equations using substitution or elimination method. Let's solve it using elimination:

Therefore, the math test consists of 5 multiple-choice questions and 15 problem-solving questions.

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Answer:

  see attached

Step-by-step explanation:

The chart shows you that w=2 when z=0. That's the point on the w-axis at lower left. Only one equation gives those results.

Answer:

  x = 7.5

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the relationship between the angle and the sides of interest is ...

  Tan = Opposite/Adjacent

  tan(37°) = x/10 . . . . fill in given values

Multiplying by 10, we get ...

  x = 10·tan(37°) ≈ 7.5

Answer:

B) 11:35 a.m.

Final answer:

The bottle will be half full at 11:50 PM, which is ten minutes before it is completely full at midnight, due to the exponential growth doubling the contents every ten minutes.

Explanation:

The question involves understanding exponential growth, specifically the doubling time of a population or, in a more tangible sense, the filling of a jar (or bottle). Given that a bottle doubles the amount inside every ten minutes and is full at midnight, we can calculate when the bottle will be half full by working backwards from the endpoint.

If the bottle is full at midnight, then it was half full at 11:50 PM, since the contents double every ten minutes. This reveals a common misunderstanding in our intuition about exponential growth, where significant change occurs in the final moments before reaching capacity.

In summary, to find out when the bottle will be half full, simply subtract a single doubling interval (ten minutes) from the time when the bottle is known to be full.

[tex]P_{ELPJ} = EK+ES+LU+LK+PV+PU JS+JV \\ \Leftrightarrow P_{ELPJ} = 2EK + 2LU + 2PV + 2JS = 2 \times 2 + 2 \times 4 + 2 \times 1 + 2 \times 2 = 18[/tex]

Answer:

Both plans last for 1.25 hours (1 hour 15 minutes)

Step-by-step explanation:

Let x hours be the time needed for plan A and y hours be the time needed for plan B.

On Wednesday there were 5 clients who did Plan A and 3 who did Plan B. Thus, 5x+3y=10.

On Thursday there were 2 clients who did Plan A and 6 who did Plan B. Thus, 2x+6y=10.

Solve the sytem of two equation. Multiply the first equation by 2, the second by 5 and subtract them:

[tex]10x+6y-10x-30y=20-50,\\ \\-24y=-30,\\ \\y=\dfrac{30}{24}=\dfrac{5}{4}=1.25\ hours.[/tex]

Therefore,

[tex]5x+3\cdot 1.25=10,\\ \\5x=10-3.75=6.25,\\ \\x=1.25\ hours.[/tex]

sadly i haven’t learned this so i can’t help you with the answers themselves but a graphing utility you could use is a graphing calculator or a graphing calculator online i know one called desmos.com just not sure if it has the intersect feature so i recommend graphing calculator

The percent that Container A is full after pumping its water into Container B until it is full is that Container A is 49.1% full after pumping water to Container B.

The problem asks us to determine what percent of Container A is full after Container B is full when water is transferred from Container A to Container B. We start by calculating the volume of both cylinders. The volume of a cylinder is given by the formula V = π r² h where V is volume, r is radius, and h is height.

Container A has a radius of 13 feet and a height of 13 feet, so:

π r² h ≈ 6985.3 cubic feet

Container B has a radius of 9 feet and a height of 14 feet, so:

π r² h≈ 3553.0 cubic feet

After filling Container B completely, the volume of water left in Container A is the original volume of Container A minus the volume of Container B. Therefore, the remaining volume in Container A is (6985.3 - 3553.0) cubic feet ≈ 3432.3 cubic feet.

To find the percentage full, we divide this remaining volume by the total volume of Container A and multiply by 100:

Percentage = (3432.3 / 6985.3) * 100 ≈ 49.1%.

After the pumping is complete, Container A is 48.4% full.

Calculate the volume of each container

The volume  of a cylinder is given by the formula:

[tex]\[V = \pi r^2 h\][/tex]

Volume of Container A

- Radius [tex]\( r_A = 13 \)[/tex]feet

- Height [tex]\( h_A = 13 \)[/tex] feet

[tex]\[V_A = \pi (13)^2 (13) = \pi (169)(13) = 2197\pi \text{ cubic feet}\][/tex]

Volume of Container B

- Radius [tex]\( r_B = 9 \)[/tex]feet

- Height [tex]\( h_B = 14 \)[/tex] feet

[tex]\[V_B = \pi (9)^2 (14) = \pi (81)(14) = 1134\pi \text{ cubic feet}\][/tex]

Calculate the remaining volume of water in Container A

Since Container A is initially full and the water is pumped into Container B until Container B is full, the remaining volume of water in Container A is:

[tex]\[V_{\text{remaining}} = V_A - V_B = 2197\pi - 1134\pi = (2197 - 1134)\pi = 1063\pi \text{ cubic feet}\][/tex]

Calculate the percent of Container A that is still full

The percent of Container A that is full is given by:

[tex]\[\text{Percent full} = \left( \frac{V_{\text{remaining}}}{V_A} \right) \times 100\%\][/tex]

Substituting the volumes we calculated:

[tex]\[\text{Percent full} = \left( \frac{1063\pi}{2197\pi} \right) \times 100\% = \left( \frac{1063}{2197} \right) \times 100\%\][/tex]

Simplifying the fraction:

[tex]\[\text{Percent full} = 0.484 \times 100\% = 48.4\%\][/tex]

Answer:

-1/2=x

Step-by-step explanation:

-9 + x = 5x - 7

     -x      -x

-9=4x-7

+7         +7

-2=4x

-2/4 =4x/4

-1/2=x

The dimensions should be 6ft by 9ft.

Final answer:

The dimensions of the floor with an area of 54 square feet, where the width is 2/3 of the length, are 9 feet in length and 6 feet in width.

Explanation:

Pascal wants to find the dimensions of a floor where the area is 54 square feet and the width is 2/3 the length. To find the dimensions, we set up an equation where the length is L and the width is W, with W = (2/3)L. Since area is calculated by the formula Area = length times width, we get 54 = L times (2/3)L. Solving this equation by multiplying the length terms and then dividing both sides by 2/3, we get L² = 54 times (3/2), which simplifies to L² = 81. Taking the square root of both sides gives us L = 9 feet. Consequently, the width would be W = (2/3) times 9 = 6 feet. Therefore, the dimensions of the floor are 9 feet by 6 feet.

Answer:

3) 2/3

4) an = 162·(1/3)^(n-1)

Step-by-step explanation:

3) A geometric sequence has a common ratio between adjacent terms. Here, that ratio is ...

r = 54/162 = 18/54 = 6/18 = 1/3

Then the next two terms can be found by multiplying by the common ratio:

6 · 1/3 = 2

2 · 1/3 = 2/3 . . . . . the sixth term

____

4) The generic expression for the n-th term of a geometric sequence with first term a1 and common ratio r is ...

an = a1·r^(n-1)

We can put in the numbers for a1 and r, and we have ...

an = 162·(1/3)^(n-1)

You can solve for 'x' in the equation 'ax = 7' by dividing both sides of the equation by 'a'. The result is 'x = 7/a'. This is based on the principle of maintaining equation equality through similar operations on both sides.

To solve for

x

in the equation

ax = 7

, you need to isolate the variable, x. This is done by

dividing

both sides of the equation by 'a'. This leaves x = 7/a. Therefore, you can find 'x' by dividing both sides of the equation by 'a'.

This process is based on the principle of equality.

You can maintain the equality of the equation by doing the same mathematical operation to both sides. Consequently, by dividing both sides by 'a', you successfully solve for x without disrupting the balance of the equation.

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Consider the attached figure. The height CD cuts the triangle exactly in half. This means that

[tex]\overline{AD}=\overline{BD}=\dfrac{1}{2}\overline{AB}=10[/tex]

Moreover, since CD is the height of the triangle, we know that ACD is a right triangle. We know the hypothenuse AC to be 20 feet because it is a side of the triangle, and we just found out that AD is 10. We can use the pythagorean theorem to deduce

[tex]\overline{CD}=\sqrt{\overline{AC}^2-\overline{AD}^2}=\sqrt{400-100}=\sqrt{300}[/tex]

So, the area is

[tex]A=\dfrac{bh}{2}=\dfrac{\overline{AB}\cdot\overline{CD}}{2} = \dfrac{20\cdot\sqrt{300}}{2}=10\sqrt{300}\approx 173[/tex]

Well to start off all sides are gonna be 20. To find area it’s lxw so 20•20=400

Dives 400 by 12 and you get 33.333333333 so you round that to the nearest whole foot and you get 33 feet

If I'm not wrong, there's no change in the measurement...  I think it's D.  since there's no visible change in the angle measurement. If it asked the coordinates then maybe I could elaborate. This question is confusing though. :/

The measure of angle Z after the transformation is D) 103°.Therefore , D.) 103​ is correct .

A translation does not change the measure of angles, so the measure of angle Z after the transformation is the same as the measure of angle Z before the transformation, which is 103°.

Image verification:

The image you sent shows a kite with the following angle measures:

Angle W = 96°

Angle X = 58°

Angle Y = 103°

Angle Z = 103°

The kite is translated up 3 units and 4 units to the right, which does not change the measure of any of the angles.

Therefore, the measure of angle Z after the transformation is still 103°.

Answer:

The correct answer options are (B) {(-6, 6), (-6, 7), (10, 12)} and (D) {(-6, 4), (10, 5)}.

Step-by-step explanation:

Here, we are given the domain {-6, 10} and we are to determine which of given relations in the options has this domain.

Domain is the set made up of the first elements of each ordered pair (x, y).

For {-6, 10} to be the domain, we will check which of the options have ordered pairs that start with -6 and 10.

If we look at option (B) {(-6, 6), (-6, 7), (10, 12)} and D. {(-6, 4), (10, 5)}, the first (two) ordered pair(s) start with -6 while the last ordered pair starts with 10.

Therefore, B and D are the correct answer option.

Answer:

6

Step-by-step explanation:

(g o f)(3) = g(f(3))

We can find f(3) using its formula with x=3:

f(3) = -2·3 +8 = -6 +8 = 2

Now, we can find g(2) using its formula with x=2:

g(2) = 3·2 = 6

So, the composition value is ...

(g o f)(3) = 6

Answer

the answer is 6/10 or 0.6

Step-by-step explanation:

6/10 (3/5) because you have to share the amount of bags into the ratio of friends which would give you 0.6 or 6/10 simplified to 3/5

Answer:

The correct answer is 3/4

Step-by-step explanation:

This is because if we first change them to using the same unit of measure we get the following.

3 ft/48 in

36 in/48 in

Now we can simplify by dividing both by 12

3/4

The lateral area and surface area of the cuboid are 72 square feet and 142 square feet, respectively. The lateral area and surface area of the prism are 42 square cm and 62 square cm, respectively.

To find the lateral area and surface area of the given cuboid and prism, we need to use the formulas for each.

For the cuboid:
1. Lateral Area: The lateral area of a cuboid can be found by adding the areas of its four side faces. Since the cuboid has a length of 7 feet, a breadth of 5 feet, and a height of 3 feet, we can calculate the lateral area as follows:
- Side 1: length * height = 7 feet * 3 feet = 21 square feet
- Side 2: breadth * height = 5 feet * 3 feet = 15 square feet
- Side 3: length * height = 7 feet * 3 feet = 21 square feet
- Side 4: breadth * height = 5 feet * 3 feet = 15 square feet
The total lateral area is the sum of these four areas: 21 + 15 + 21 + 15 = 72 square feet.

2. Surface Area: The surface area of a cuboid is found by adding the areas of all six faces. In addition to the lateral area, we need to include the areas of the top and bottom faces. Using the dimensions of the cuboid, we can calculate the surface area as follows:
- Top face: length * breadth = 7 feet * 5 feet = 35 square feet
- Bottom face: length * breadth = 7 feet * 5 feet = 35 square feet
The total surface area is the sum of these six areas: 72 (lateral area) + 35 (top face) + 35 (bottom face) = 142 square feet.

Now, for the prism:
1. Lateral Area: To find the lateral area of the prism, we need to find the perimeter of the base and multiply it by the height of the prism. Since the prism has a base with a length of 5 cm and a breadth of 2 cm, the perimeter is: 2 * (length + breadth) = 2 * (5 cm + 2 cm) = 2 * 7 cm = 14 cm.
The lateral area is obtained by multiplying the perimeter by the height: 14 cm * 3 cm = 42 square cm.

2. Surface Area: The surface area of the prism is the sum of the lateral area and twice the area of the base. Since the base is a rectangle with a length of 5 cm and a breadth of 2 cm, its area is: length * breadth = 5 cm * 2 cm = 10 square cm.
The surface area is then calculated as: 42 (lateral area) + 2 * 10 (area of the base) = 42 + 20 = 62 square cm.

Answer:

The volume would be 1 1/4 cubic inches.

Step-by-step explanation:

To find this, multiply all three numbers together because the formula for volume is length multiplied by width multiplied by height.

V = lwh

V = (1/4)(1 1/4)(4)

V = 1 1/4

[tex]\bf a^{2b}\implies a^{2\cdot b}\implies (a^2)^b\implies (a^b)^2\qquad \boxed{a^b=x}\qquad (x)^2\implies x^2[/tex]

Answer:

8. A'(-1/2, 1), B'(0, 0), C'(1, 1 1/2)

10. 20°, 60°, 100°

Step-by-step explanation:

8. Point B is at the origin, the center of dilation, so its coordinates remain unchanged. The coordinates of A and C are each multiplied by the scale factor, 1/2.

A' = (1/2)A = (1/2)(-1, 2) = (-1/2, 1)

C' = (1/2)C = (1/2)(2, 3) = (1, 3/2)

__

10. The total number of ratio units is 1+3+5 = 9. The total of angle measures in any triangle is 180°. So, each of the "ratio units" must stand for 180°/9 = 20°. Then the angles are ...

1 · 20° = 20°

3 · 20° = 60°

5 · 20° = 100°

To determine the dimensions of the wall, we set up an equation using the given area and the fact that the wall's height is 2/3 of its length. Solving for length and height, we find that the length is 30 feet and the height is 20 feet.

The question asks to determine the length and height of a wall that Leo wants to paint, given that the area of the wall is 600 square feet, and the height is 2/3 of its length. To solve this, we will set up an equation to represent the relationship between the length and height and use the area to find the specific dimensions.

Let's use L to represent the length of the wall and H to represent the height. According to the given information, H = (2/3)L. The area of a rectangle is calculated by multiplying its length by its height, so we can set up the equation:

Area = L \H = 600 sq ft

Substituting the height with its relation to length, we get:

600 = L \(2/3)L

Dividing both sides by L and then by 2/3, we find that:

L² = 600 \(3/2)

L² = 900

L = 30 ft (since length must be positive)

Now, to find the height:

H = (2/3)\L = (2/3) \ 30 = 20 ft

So, the length of the wall is 30 feet and the height is 20 feet.

It would be located at (1, 3). Hope this helps!

Answer:

1,3

Step-by-step explanation:

Answer:

standard deviation will remain unchanged at 3.5

Step-by-step explanation:

Subtracting 2 from each of the values in the data set will only change the origin of the data set. The mean of the values will change but the variance and consequently the standard deviation will remain unchanged

Answer:

standard deviation of the resulting data will be 3.5

Step-by-step explanation:

When we add or subtract each values of the data set by some constant then the mean will change by the same amount whereas the there is no change in the standard deviation.

So, when we subtract 2 from each values of the data set, the standard deviation of the resulting data will be also 3.5.